Maurice has 4/5 of a bag of popcorn left to share with his 2 brothers. If each of the three brothers will get the same amount, how much of the bag will each person get?

There are 1 + 2 = <<1+2=3>>3 people who will share 4/5 of a bag of popcorn.

So, each person will get 4/5 ÷ 3 = 4/5 × 1/3 = <<4/5*1/3=4/15>>4/15 of a bag. Answer: \boxed{\frac{4}{15}}.